Q. 153.9( 10 Votes )

A two–digit number is 5 times the sum of its digits and is also equalto5 more than twice the product of its digits. Find the number.

Answer :

Let the units digit be ‘Y’, so the tens digit will be X.


the number is 10X + Y


10X + Y = 5 (X + Y)


On simplifying further,


10X – 5X – 5Y + Y = 0


5X – 4Y = 0 –––––– (i)


10X + Y = 2XY + 5


10X– 2XY + Y – 5 = 0 –––––– (ii)


Putting the value of from equation –––––– (i)



40Y – 8Y2 + 5Y – 25 = 0


8Y2 – 45Y + 25 = 0


On applying Sreedhracharya formula







Y = or 5


Y = 5


from equation (i)


X = 4


The number is 45 {4(10)+5}.


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